# How do I find the dot product of vec(u)+vec(v) and vec(u)−vec(v) ?

How do I find the dot product of $\stackrel{\to }{u}+\stackrel{\to }{v}$ and $\stackrel{\to }{u}-\stackrel{\to }{v}$ with the given information?
I already know that $|\stackrel{\to }{u}|=2,|\stackrel{\to }{v}|=3,|$ and $⟨\stackrel{\to }{u},\stackrel{\to }{v}⟩=1$. I am unsure as to how to proceed in order to find $⟨\stackrel{\to }{u}+\stackrel{\to }{v},\stackrel{\to }{u}-\stackrel{\to }{v}⟩$
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Marlene Welch
We have that
$\left(u+v\right)\cdot \left(u-v\right)=u\cdot \left(u-v\right)+v\cdot \left(u-v\right)=u\cdot u-u\cdot v+v\cdot u-v\cdot v=...$
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Sariah Mcguire
HINT:
$\left(u+v,u-v\right)=\left(u,u\right)-\left(u,v\right)+\left(v,u\right)-\left(v,v\right)$
You know all of the terms of the RHS of the previous equation.